Class 4 Notes - Geometry

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Introduction to Geometry

Geometry is the branch of mathematics that deals with shapes, sizes, positions, and properties of space. It helps us understand and describe the world around us using figures and patterns.

Types of Lines

  • Straight Line: The shortest distance between two points.
  • Curved Line: A line that is not straight.
  • Parallel Lines: Lines that never meet, no matter how far they are extended.
  • Intersecting Lines: Lines that cross each other at a point.
  • Perpendicular Lines: Lines that meet at a right angle (90°).

Plane Figures (2-D Shapes)

  • Triangle: 3 sides, 3 corners.
  • Square: 4 equal sides, 4 right angles.
  • Rectangle: 4 sides, opposite sides equal, 4 right angles.
  • Circle: No sides or corners, all points are at equal distance from the center.
  • Polygon: A closed figure with three or more straight sides (e.g., pentagon, hexagon).

Solid Figures (3-D Shapes)

  • Cube: 6 square faces, 12 edges, 8 corners.
  • Cuboid: 6 rectangular faces, 12 edges, 8 corners.
  • Sphere: Round, no edges or corners (e.g., ball).
  • Cylinder: 2 circular faces, 1 curved surface (e.g., can, bottle).
  • Cone: 1 circular base, 1 curved surface, 1 vertex (e.g., ice-cream cone).

Properties of Shapes

  • Vertices (Corners): Points where two or more edges meet.
  • Edges: Line segments between two vertices.
  • Faces: Flat or curved surfaces of a solid shape.

Symmetry

A shape is symmetrical if it can be divided into two identical halves. The dividing line is called the line of symmetry.

  • Square, rectangle, and circle have symmetry.
  • Some shapes have more than one line of symmetry.

Patterns

Patterns are repeated designs or sequences using shapes, colors, or numbers. Recognizing patterns helps in understanding geometry and mathematics.

Real-Life Examples

  • Wheels (circle), bricks (cuboid), dice (cube), traffic signs (triangle, rectangle, circle).
  • Tiles on the floor show patterns and symmetry.

Word Problems

Problem: How many corners does a rectangle have?

Solution: A rectangle has 4 corners.

Problem: Name a solid shape that has only one curved surface.

Solution: Sphere.

Summary

Geometry helps us recognize and describe shapes and patterns in our surroundings. Understanding lines, shapes, and their properties is useful in daily life and problem-solving.